Explore chaos in this simulation of two double pendulums, where small differences in the release angles produce wildly different outcomes.

Explore chaos in this simulation of two double pendulums, where small differences in the release angles produce wildly different outcomes.

Visualize chaos with the orbit of three or more objects bound by gravity

In this simulation, users can simulate randomized and preset orbital configurations for up to 10 celestial bodies to observe the system's evolution in an interactive 3D space. The same configurations can produce different orbital behavior—a feature of chaos—by making small changes to an object's mass under advanced settings.

Explore interactive simulations of strange attractors, the graphs that help visualize chaos

Although simple, linear equations reach an explicit value for a given input, such as *f(x) \= x* + 1 equaling 4 when *x* equals 3, some chaotic, nonlinear systems tend to evolve towards multiple values simultaneously. These simulations allow users to observe the unusual mathematical artifacts created by systems as their outputs evolve toward these distinct values.

The life of Edward Lorenz, who originally used a seagull in his 'butterfly effect' metaphor

By accidentally finding that rounding one variable to its third decimal place and re-running a weather simulation produced a drastically different two-month forecast, the American mathematician established the field of chaos theory. His paper—"Predictability: Does the Flap of a Butterfly's Wings in Brazil Set off a Tornado in Texas?"—introduced the well-known metaphor for the behavior of chaotic systems. (Some readers may experience a paywall.)

Explore the effects of tornadoes of different scales

In this simulation, users can adjust the tornado's diameter and rotation speed to see its impact as it passes through a series of trees and a one-story home.

Chaos theory—informally known as the butterfly effect—is the reason why weather forecasts are presented with probabilities rather than certainties.

Play an incremental game that teaches the history of particle physics

Developed during the CERN Summer Student Webfest 2014, this game tasks you with building the reputation of your particle accelerator as you discover particles and hire staff to collect data. A historical breakdown accompanies each discovery, allowing you to recreate the timeline of the field.

Researchers identify a hidden instability pattern in simple ocean wave models

Stokes waves—a solution to the mathematics of water waves—were once assumed to be stable. Italian mathematicians have proven disturbances cause these waves to collapse and such collapses follow an infinite repeating pattern. To complete the proof, the team offered a $100 donation to solicit online help.

Simulate the impact of an antimatter bomb around the world

Using "Total Annihilator," users can click on a location on the map, select the antimatter mass, and the observation altitude before detonating the bomb. Scrolling through the left sidebar reveals the impacts of the detonation, including the sizes of the resulting fireball and thermal pulse, the spread of ionizing radiation, and the atmospheric effects.

Simulate the precession of Mercury's perihelion

The location of Mercury's closest point to the sun shifted in the sky at a rate of approximately 0.16 degrees per century, or 0.012 degrees more than what was predicted by Isaac Newton due to the gravity of the other planets. General relativity correctly predicted this shift.

LIGO boosts its signal sensitivity by manipulating quantum uncertainty

According to the uncertainty principle, the amplitude, or height of a wave's peak, and its phase—the point in time when the first peak is observed—are inversely linked. Based on the frequency of the gravitational waves of interest, scientists sacrifice precision in one optical property to reduce noise in another.

Counterweights can dampen the impact of seismic activity on buildings

Japan’s Tokyo Skytree uses a free-moving central column inspired by ancient pagodas, while Taiwan’s Taipei 101 contains a 660-ton pendulum on its 92nd floor that swings out of sync with the building.

How a competition honoring a king's birthday uncovered history's first chaotic system

A committee established a contest for King Oscar II's 60th birthday, featuring four unsolved problems in mathematics, including one on proving the stability of a system of more than two objects held together by gravity. Focusing on three celestial objects, Henri Poincaré won the prize for his proof, which he later learned was incorrect and, upon correcting it, instead proved these systems to be unstable.

The double-slit experiment is observational evidence for the wave-particle duality

Light and electrons can behave like particles when observed, but they also exhibit wave-like properties in motion, creating patterns through interference. Even larger objects, such as baseballs, have wavelengths, but they are negligibly small compared to their size.

Explore a simulation of ideal gas behavior, which can be explained by kinetic molecular theory

The theory describes particles as moving in random directions, with a distribution of velocities determined by the gas's temperature. The particles collide elastically like billiard balls, are negligibly small, and do not exert forces on one another. The gas laws can be derived from these principles using statistics or observed via this interactive.

Boomerang earthquakes reverse direction and ripple back the way they came

Computer simulations show that rapid changes in friction along a fault where an earthquake has traveled for long distances can produce a smaller quake in the opposite direction. Data consistent with the phenomena has only been recorded a handful of times from 2011 to 2023.

Objects moving relative to one another will not agree on the simultaneity of events

Space and time shift when switching from a nonmoving to a moving perspective, causing events that seem to occur simultaneously for one person not to appear that way for someone else. This also means one person's present could be another's future, ensuring all of time already exists.

The magic angle to skip a spinning stone is 20 degrees

The traditional shoreside activity—reputedly practiced by luminaries Shakespeare and Homer—can be broken down into its bare physics, from hydrodynamics and momentum to gravity.

Test your gerrymandering skills with this interactive game

This simulation demonstrates how packing and cracking alter election outcomes. See how shifting district lines can change representation—regardless of the overall makeup of the electorate.

Use this day trading simulator to practice buying and selling stocks while leveraging real-time data and trading charts

Want to try day trading but don't want to risk losing cash? This simulator gives users access to "unlimited" fake money, as well as the option to convert their simulation accounts to the real deal later on.

Calibrate to the U.S. government's official clock, synchronized to the atomic standard

The site displays the current time across all American time zones—corrected for network delay—and shows whether your device's clock has drifted. Computer clocks rely on quartz crystals that drift slightly with temperature and age, requiring alignment with atomic clocks (which are so stable that seconds are defined by them).

There are more chess game variations than observable atoms in the universe

Mathematician Claude Shannon estimated there are 10 to the 120th power variations of chess games possible. Known as the "Shannon number," this is more than the estimated number of atoms in the cosmos.

The world's different calendars, explained

The calendar we use to mark the days, months, and year can feel set in stone, but the history of calendars shows these organization systems can and do change. Parse the fascinating, complex details of the Gregorian, Julian, Chinese, Hebrew, and many more calendars in this comprehensive, well-executed explainer video.

Listen to the sounds of pulsars, which emit radio pulses up to hundreds of times a second

Just as figure skaters spin faster by tucking in their arms, these celestial objects acquire high rates of spin from the collapse of the cores of massive stars. The star's rotation spins its magnetic field, generating beams of radio waves from its magnetic poles. If either of these poles faces a detector, the signals can be picked up and converted to audio signals.

Simulation of the coronavirus inside an aerosol droplet

A new simulation shows how the virus survives inside tiny airborne particles of water — and gives clues about how the Delta variant became dominant.

Inside MLB's robo-umping experiment

Human umpires call roughly 94% of pitches right overall, but performance reduces on borderline pitches in high-leverage moments, the calls that shape game outcomes most. A professor and historian analyze early experiments with the full "robot ump" system that helped shape MLB's decision to implement a compromise "challenge" system.

Explore hindcasting on climate models published since 1972

Hindcasting tests model forecasts against observational data to determine their accuracy. In this interactive, you can learn about the differences between eight climate models and evaluate them against available climate data.

Explore our favorite visualization of the immense scale of space, from an astronaut to the size of the observable universe

Planeterrellas create artificial auroras that mimic the atmospheric displays of light by setting up an electric field between two metal balls in a jar filled with a small amount of air.

Visualize the path of every solar eclipse from 1900 to 2099 and see what each looks like when observed from different locations on Earth.

Play the role of a student in a game where you try to navigate college and remain debt-free, selecting different income levels, high school experience, race, ethnicity, and more.

Learn how your body is, scientifically, like a firework with its own slow, controlled burn.

Visualize how CRISPR-Cas9—a type of immune system used by single-celled organisms to attack invasive viruses—targets and makes precise changes to a gene's DNA.

A pickleball's loud 'pop' sound can reach 120 decibels, which is equivalent to a hammer hitting a nail

While the sun's gravity keeps the planets in orbit, their gravity also pulls on the sun, causing it and everything else in the solar system to orbit around a mutual balance point called the barycenter—the true center of the solar system.

For centuries, it was common to sleep in two shifts: a few hours at the beginning of the night, and a longer period beginning around midnight

Exploring the Larry Bird punch that almost changed March Madness

For centuries, Niagara Falls has been a magnet for daredevils seeking to conquer one of nature's most powerful wonders, with its 200-foot drop and water rushing at 32 feet per second with 280 tons of force.

Radioactive elements can introduce software errors because the ionizing radiation they produce can detach electrons from atoms, and computer code relies on the distribution of electrons.

After 25 people used virtual reality headsets to practice flying with virtual wings—flapping their arms—their visual cortex responded to the wings almost as if they were real arms, treating them as body parts.

Clever Hans was a 1900s horse that was believed to be able to solve math equations, tell time, and read and comprehend German, until a psychology student discovered how he got his answers.

Coral polyps reproduce via broadcast spawning, where entire reefs simultaneously release reproductive cells for about one hour, once a year.

English mathematician Ada Lovelace wrote the first computer algorithm a century before computers existed and hypothesized that computing devices would one day be able to compose music—foreseeing the generative AI systems of today.

Search a massive database of over 4 decades of clues from the TV quiz show 'Jeopardy!'

How Amazon operates a 'flywheel' business model, a self-reinforcing cycle that drives continuous growth

Hedge funds, the private investment firms that trade a wide swath of financial assets, make money by imposing steep fees on investors and from the fund's investment performance.

Hear 50 years of iconic hip-hop samples, the genre's foundational looped tracks

In 1945, Surrealist artist Salvador Dalí and legendary animator Walt Disney began collaborating on a short film that was not completed until 2003, years after both men had died.

See a ranking of the best (and worst) Federal Reserve Chairs since 1914 out of the 16 men and women who have held the office since.

The word 'jazz' evolved from 'jasm,' 19th-century American slang for 'energy'